About

Jonathan Freund is the Willett Professor and Department Head of Aerospace Engineering at the University of Illinois Urbana-Champaign. He holds a Ph.D. in Mechanical Engineering from Stanford University, obtained in 1998, and has held various academic positions including Professor and Associate Professor in both Aerospace Engineering and Mechanical Science and Engineering at UIUC. Freund's research interests encompass uncertainty quantification, large-scale parallel computing, numerical methods, biological and biomedical fluid dynamics, mechanics of nanometer-scale systems, aerodynamics, and fluid mechanics. His work has contributed to the understanding of complex fluid flows, aeroacoustics, combustion and propulsion, and computational fluid mechanics. Freund has authored chapters in books and numerous articles in peer-reviewed journals, focusing on topics such as blood cell interactions, jet noise prediction, and shock-to-detonation transition modeling. He is actively involved in interdisciplinary research centers and laboratories, advancing the fields of aerospace and fluid dynamics through innovative computational and experimental approaches.

Research topics

• Physics
• Optics
• Artificial Intelligence
• Materials science
• Computer Science
• Mathematics
• Mathematical optimization
• Aerospace engineering
• Thermodynamics
• Geology
• Mechanics
• Applied mathematics
• Algorithm
• Chemistry
• Engineering
• Mathematical analysis
• Optoelectronics

Selected publications

• Corrigendum to “A TVD neural network closure and application to turbulent combustion” [Journal of Computational Physics 523 (2025)/113638]

  Journal of Computational Physics · 2025-02-07

  erratumOpen accessSenior author
  PublisherDOI

• Pyrometheus: Symbolic abstractions for XPU and automatically differentiated computation of combustion kinetics and thermodynamics

  ArXiv.org · 2025-03-31

  preprintOpen accessSenior author

  The cost of combustion simulations is often dominated by the evaluation of net production rates of chemical species and mixture thermodynamics (thermochemistry). Execution on computing accelerators (XPUs) like graphic processing units (GPUs) can greatly reduce this cost. However, established thermochemistry software is not readily portable to such devices or sacrifices valuable analytical forms that enable differentiation for sensitivity analysis and implicit time integration. Symbolic abstractions are developed with corresponding transformations that enable computation on accelerators and automatic differentiation by avoiding premature specification of detail. The software package Pyrometheus is introduced as an implementation of these abstractions and their transformations for combustion thermochemistry. The formulation facilitates code generation from the symbolic representation of a specific thermochemical mechanism in multiple target languages, including Python, C++, and Fortran. Computational concerns are separated: the generated code processes array-valued expressions but does not specify their semantics. These semantics are provided by compatible array libraries, such as NumPy, Pytato, and Google JAX. Thus, the generated code retains a symbolic representation of the thermochemistry, which translates to computation on accelerators and CPUs and automatic differentiation. The design and operation of these symbolic abstractions and their companion tool, Pyrometheus, are discussed throughout. Roofline demonstrations show that the computation of chemical source terms within MFC, a Fortran-based flow solver we link to Pyrometheus, is performant.

  PublisherOA PDFDOI

• MIRGE: An Array-Based Computational Framework for Scientific Computing

  ArXiv.org · 2025-12-18

  articleOpen access

  MIRGE is a computational approach for scientific computing based on NumPy-like array computation, but using lazy evaluation to recast computation as data-flow graphs, where nodes represent immutable, multi-dimensional arrays. Evaluation of an array expression is deferred until its value is needed, at which point a pipeline is invoked that transforms high-level array expressions into lower-level intermediate representations (IR) and finally into executable code, through a multi-stage process. Domain-specific transformations, such as metadata-driven optimizations, GPU-parallelization strategies, and loop fusion techniques, improve performance and memory efficiency. MIRGE employs "array contexts" to abstract the interface between array expressions and heterogeneous execution environments (for example, lazy evaluation via OpenCL, or eager evaluation via NumPy or CuPy). The framework thus enables performance portability as well as separation of concerns between application logic, low-level implementation, and optimizations. By enabling scientific expressivity while facilitating performance tuning, MIRGE offers a robust, extensible platform for both computational research and scientific application development. This paper provides an overview of MIRGE. We further describe an application of MIRGE called MIRGE-Com, for supersonic combusting flows in a discontinuous Galerkin finite-element setting. We demonstrate its capabilities as a solver and highlight its performance characteristics on large-scale GPU hardware.

  PublisherOA PDF

• Conceptual Design and Optimization of a Scramjet with Ablative Thermal Protection

  2025-07-16

  articleSenior author

  The design of supersonic-combustion ramjet (scramjet) engines requires approaches that account for both the system performance and the complex interactions of the engine components. At the system level, the propulsor must meet the inherent performance needs such as specific-impulse (I_sp) or propulsion efficiency (\eta_p) for a given vehicle geometry and flight trajectory. Simultaneously, each subsystem--including the inlet, combustor, and nozzle--must operate efficiently to contribute to the system-level behavior while each adhering to its own physical and operational constraints. Thermal management is a critical aspect of the engine, that we particularly address by introducing novel ablative materials used as thermal protection systems (TPS), capable of withstanding the extreme heat loads typical of supersonic combustion. This work presents the development and coupling of reduced models that balance fidelity with computational efficiency for early-stage design and eventual multidisciplinary design optimization (MDO) of scramjets. The proposed models predict critical failure modes such as unstart and thermal overload. In particular, we implement quasi-one-dimensional models to characterize the gas thermodynamics along the engine flowpath, coupled with a low-dimensional unsteady model of gas-wall interactions in the combustor to evaluate the ablative materials performance. The model reproduces key propulsion and material performance parameters to support the analysis of trade-offs for design and it provides a foundation for optimizing scramjets due to its modularity and moderate accuracy.

  PublisherDOI

• MIRGE: An Array-Based Computational Framework for Scientific Computing

  arXiv (Cornell University) · 2025-12-18

  preprintOpen access

  MIRGE is a computational approach for scientific computing based on NumPy-like array computation, but using lazy evaluation to recast computation as data-flow graphs, where nodes represent immutable, multi-dimensional arrays. Evaluation of an array expression is deferred until its value is needed, at which point a pipeline is invoked that transforms high-level array expressions into lower-level intermediate representations (IR) and finally into executable code, through a multi-stage process. Domain-specific transformations, such as metadata-driven optimizations, GPU-parallelization strategies, and loop fusion techniques, improve performance and memory efficiency. MIRGE employs "array contexts" to abstract the interface between array expressions and heterogeneous execution environments (for example, lazy evaluation via OpenCL, or eager evaluation via NumPy or CuPy). The framework thus enables performance portability as well as separation of concerns between application logic, low-level implementation, and optimizations. By enabling scientific expressivity while facilitating performance tuning, MIRGE offers a robust, extensible platform for both computational research and scientific application development. This paper provides an overview of MIRGE. We further describe an application of MIRGE called MIRGE-Com, for supersonic combusting flows in a discontinuous Galerkin finite-element setting. We demonstrate its capabilities as a solver and highlight its performance characteristics on large-scale GPU hardware.

  PublisherDOI

• Acoustically excited bubble tunnelling through soft material

  Journal of Fluid Mechanics · 2025-10-07

  articleOpen accessSenior author

  Experiments have shown that ultrasound-stimulated microbubbles can translate through gel phantoms and tissues, leaving behind tunnel-like degraded regions. A computational model is used to examine the tunnelling mechanisms in a model material with well-defined properties. The high strain rates motivate the neglect of weak elasticity in favour of viscosity, which is taken to degrade above a strain threshold. The reference parameters are motivated by a 1 $\unicode{x03BC}$ m diameter bubble in a polysaccharide gel tissue phantom. This is a reduced model and data are scarce, so close quantitative agreement is not expected, but tunnels matching observations do form at realistic rates, which provides validation sufficient to analyse potential mechanisms. Simulations of up to 100 acoustic cycles are used to track tunnelling over 10 bubble diameters, including a steady tunnelling phase during which tunnels extend each forcing cycle in two steps: strain degrades the tunnel front during the bubble expansion, and then the bubble is drawn further along the tunnel during its subsequent inertial collapse. Bubble collapse jetting is damaging, though it is only observed during a transient for some initial conditions. There is a threshold behaviour when the viscosity of the undamaged material changes the character of the inertial bubble oscillation. Apart from that, the tunnel growth rate is relatively insensitive to the high viscosity of the material. Higher excitation amplitudes and lower frequencies accelerate tunnelling. That acoustic radiation force, elasticity and bubble jetting are not required is a principal conclusion.

  PublisherDOI

• Bayesian Model Selection for Graphite Oxidation by Molecular Oxygen

  SSRN Electronic Journal · 2025-01-01

  preprintOpen accessSenior author
  PublisherDOI

• A TVD neural network closure and application to turbulent combustion

  Journal of Computational Physics · 2024-12-02 · 2 citations

  articleOpen accessSenior author

  Trained neural networks (NN) have attractive features for closing governing equations. There are many methods that are showing promise, but all can fail in cases when small errors consequentially violate physical reality, such as a solution boundedness condition. A NN formulation is introduced to preclude spurious oscillations that violate solution boundedness or positivity. It is embedded in the discretized equations as a machine learning closure and strictly constrained, inspired by total variation diminishing (TVD) methods for hyperbolic conservation laws. The constraint is exactly enforced during gradient-descent training by rescaling the NN parameters, which maps them onto an explicit feasible set. Demonstrations show that the constrained NN closure model usefully recovers linear and nonlinear hyperbolic phenomena and anti-diffusion while enforcing the non-oscillatory property. Finally, the model is applied to subgrid-scale (SGS) modeling of a turbulent reacting flow, for which it suppresses spurious oscillations in scalar fields that otherwise violate the solution boundedness. It outperforms a simple penalization of oscillations in the loss function. • Neural networks embedded in PDEs can violate physical bounds unless constrained. • Motivated by established schemes, a new neural network approach is introduced. • It is demonstrated for subgrid-scale modeling for turbulent combustion.

  PublisherDOI

• A TVD neural network closure and application to turbulent combustion

  arXiv (Cornell University) · 2024-08-06

  preprintOpen accessSenior author

  Trained neural networks (NN) have attractive features for closing governing equations. There are many methods that are showing promise, but all can fail in cases when small errors consequentially violate physical reality, such as a solution boundedness condition. A NN formulation is introduced to preclude spurious oscillations that violate solution boundedness or positivity. It is embedded in the discretized equations as a machine learning closure and strictly constrained, inspired by total variation diminishing (TVD) methods for hyperbolic conservation laws. The constraint is exactly enforced during gradient-descent training by rescaling the NN parameters, which maps them onto an explicit feasible set. Demonstrations show that the constrained NN closure model usefully recovers linear and nonlinear hyperbolic phenomena and anti-diffusion while enforcing the non-oscillatory property. Finally, the model is applied to subgrid-scale (SGS) modeling of a turbulent reacting flow, for which it suppresses spurious oscillations in scalar fields that otherwise violate the solution boundedness. It outperforms a simple penalization of oscillations in the loss function.

  PublisherOA PDFDOI

• Combustion Heat Flux Estimation for Design of Carbon Fiber-Based Thermal Protection Systems

  2024-07-27

  articleSenior author

  Thermal protection systems are essential to withstand the large aerothermal loads of hypersonics flow environments. This approach is investigated for hypersonic propulsion using scramjets, where the combustor walls must be insulated against hot gaseous combustion products in addition to high temperatures from supersonic flow deceleration. Weight is key for flight, so an attractive option is protection with light-weight carbon-phenolic composite materials, where the phenolic resin degrades by pyrolysis reactions, producing gases that flow toward the surface. The analysis of flame-exposed lightweight carbon fiber insulators is performed with experiments and numerical simulations of a controlled environment. Our setup uses the McKenna flat flame burner, which creates a steady, laminar flame where combustion products interact with test materials. This configuration allows a controlled assessment of fluid-wall interaction and consequent degradation of the test samples without the complexity of supersonic turbulent mixing. Initial validation of a coupled combustion flow/material model is presented.

  PublisherDOI

Recent grants

• Order and chaos in the flow of red blood cells

  NSF · $280k · 2013–2017

• The multi-cell fluid mechanics of white cell transport in microvessels

  NSF · $278k · 2009–2013

• The Atomic Detail of Evaporating Menisci

  NSF · $230k · 2005–2009

Frequent coauthors

• Daniel J. Bodony

  University of Illinois Urbana-Champaign

  40 shared

• Carlos Pantano

  Southern California University for Professional Studies

  34 shared

• Harley T. Johnson

  25 shared

• Mingjun Wei

  Kansas State University

  23 shared

• Gregory Elliott

  University of Illinois Urbana-Champaign

  23 shared

• Peter Jordan

  Institut Pprime

  21 shared

• Parviz Moin

  Stanford University

  20 shared

• David Buchta

  Johns Hopkins University

  20 shared

Labs

• Gas Dynamics LaboratoryPI

Education

• Ph.D., Aerospace Engineering

  University of Illinois at Urbana-Champaign

  1990

• M.S., Aerospace Engineering

  University of Illinois at Urbana-Champaign

  1986

• B.S., Aerospace Engineering

  University of Illinois at Urbana-Champaign

  1984

Awards & honors

• Kritzer Faculty Scholar, August 16, 2011-2016